TRIPOLI, Lebanon — Deep in a violent and lawless slum just north of this coastal city, 12 men whose faces were shrouded by scarves drilled with Kalashnikovs. In unison, they lunged in one direction, turned and lunged in another. “Allah-u akbar,” the men shouted in praise to God as they fired their machine guns into a wall. The men belong to a new militant Islamic organization called Fatah al Islam, whose leader, a fugitive Palestinian named Shakir al-Abssi, has set up operations in a refugee camp here where he trains fighters and spreads the ideology of Al Qaeda. He has...